High energy particle in a random time dependant potential

We study the long time behaviour of the speed of a particle moving in Rd under the influence of a random time-dependent potential representing the particle’s environment. The particle undergoes successive scattering events that we model with a Markov chain for which each step represents a collision. As the potential depends on time, the kinetic energy of the particle is non bounded and expected to grow in time. Assuming the initial velocity is large enough, we show that, with high probability, the particle’s kinetic energy E(t) grows as t2/5 when d>5. We will also see for which time rescaling, macroscopic change of energy and direction can be seen.